Parboil the sausages in a few inches of water until cooked through, about 20 minutes. Meanwhile, preheat an outdoor grill, indoor griddle or cast-iron pan to medium-high heat.
While the grill heats up, add 2 tbsp. EVOO, a couple turns of the pan, to a large skillet over medium heat. Add the sliced fennel, onion, garlic and thyme; season with salt and pepper. Cook until tender, 12 to 15 minutes. Deglaze with the Pernod or St-Germain, then with the white wine; reduce the liquids at a simmer for about 10 minutes.
Meanwhile, split the sausages lengthwise but do not cut through; drizzle with EVOO. Grill the sausages on both sides. Place in the sub rolls and top with the fennel-onion mixture and cheese; garnish with the basil or tarragon, reserved fennel fronds and parsley.